Put them in a pot of boiling water, cover, turn off the heat, and leave covered for about 10 minutes.
I usually run the cooked egg under some cold water to make it easier to handle. Tap it on the countertop and peel the shell. Older (still good, of course) eggs will peel more easily than the freshest.
Put the eggs in a pot with enough water to just cover them. Heat the water until it just starts to boil, then turn off the heat and move the pot off the stove. Once the water is cool enough to stick your hand in, they're done.
You know how you sometimes get that grey ring around the yolk? I think it's because you use either hot or cold water. It's one or the other, but I don't remember.
Heat water to just below boiling.
Place eggs in water with enough heat to keep it almost boiling.
Do not let the water get to a rolling boil.
Cook for 17 minutes.
Take out and place eggs in a bowl of water/ice cubes.
Let sit for 5 minutes.
Shell eggs.
Another tip is if you take a tack and poke a hole in the large end of the egg before you place it in boiling water the yolks will not turn green. The hole allows the sulphur to escape while the eggs cook.